In a pulley sytem with 100% effieciency with ten support cables. The input side reels 100 meters of cable. How far dis the output move?

What is the value of the output force?

In identical conditions at 70% efficiency, the cable does not stretch. How much input force is needed to perform same output work?

To determine the distance the output moves in a pulley system with 100% efficiency and ten support cables, we can use the concept of a balanced pulley system. In a balanced system, the length of cable pulled in by the input side is equal to the length of cable let out by the output side.

In this case, the input side reels in 100 meters of cable. Since the system has 100% efficiency, the output side will also let out 100 meters of cable.

Therefore, the distance the output moves is 100 meters.

Next, let's find the value of the output force. In an ideal pulley system with no friction and 100% efficiency, the input force is equal to the output force. This is based on the principle of work conservation.

Hence, the value of the output force is the same as the input force in this 100% efficient pulley system.

Now, let's consider the conditions where the system has a 70% efficiency but the cable does not stretch. In this case, we will use the concept of work conservation to determine the input force needed to perform the same output work.

Work is defined as the product of force and distance. If the output work remains constant, the product of the output force and the distance moved by the output must be equal to the product of the input force and the distance moved by the input.

Let's assume the input force is F1, and the distance moved by the input is D1.

The output force is equal to the input force multiplied by the efficiency (70% or 0.7). Hence, the output force is F2 = F1 * 0.7.

Since the cable does not stretch, the distance moved by the input is the same as the distance moved by the output. Therefore, D1 = D2.

From work conservation, we can write the equation: F1 * D1 = F2 * D2.

Substituting the values, we get F1 * D1 = (F1 * 0.7) * D1.

Simplifying the equation, we find F1 = (F1 * 0.7).

To solve for F1, we divide both sides of the equation by 0.7:

F1 = F1 / 0.7.

Therefore, to perform the same output work with 70% efficiency and a non-stretching cable, the input force needed is approximately equal to the output force divided by 0.7 (or 1/0.7).